Name Answer Key
1
Here is a birthday cake cut into pieces.
How many pieces do you see?
ANSWER: 24 pieces
COMMENTS & EXTENSIONS: Trace your hand on graph
paper. How many of the graph paper squares does your
hand cover? Which is bigger, your hand or your foot? Trace
your foot and count the squares it covers.
© ETA hand2mind™
Equivalent Fractions and Decimals ■ Lesson 1
Hands-On Standards® Fractions
Lesson
1
Name Same Height
Answer Key
Try This
■■
Model the first fraction using Fraction Tower Cubes.
■■
Use hints to model an equivalent fraction.
■■
Fill in the answer blanks.
6
1
2. ​ __
 ​ = ​ ___   ​ 
3
12
3
1.​ __
 ​ = ​ __  ​
4
8
yellow
6
3 _______­
= ___
blue
4
Model
equivalent
fraction.
1
4
black
___
orange = ___
_______
2
4
  ​ = ​ __  ​
4.​ ___
5
10
8
  ​ = ​ __  ​
3.​ ___
6
12
Model
first
fraction.
4
8
4
teal
___
black = ___
_______
4
purple
2
green
___
_______
= ___
_______
9
3
 ​ = ​ ___   ​ 
5.​ __
4
12
4
2
 ​ = ​ __  ​
6.​ __
6
3
5
1
 ​ = ​ ___   ​ 
7. ​ __
2
10
6
3
 ​ = ​ ___   ​ 
8. ​ __
5
10
2
  ​ = __
​  14 ​
9.​ __
8
2
6
  ​ = ​ __  ​
10.​ ___
4
12
© ETA hand2mind™
Challenge
Find an equivalent fraction without using cubes. Show your work.
10
1
 ​ = ​ ___   ​ 
​ __
2
20
__
​  14 ​ =
4
​ ___
   ​ 
16
Equivalent Fractions and Decimals ■ Lesson 1
__
​  23 ​ =
6
​ __
  ​
9
1
4
​ ___
  ​ = ​ __  ​
5
20
___
​  10
  ​ =
15
2
​ __
  ​
3
Hands-On Standards® Fractions
Lesson
1
Name Same Height
Answer Key
Use Fraction Towers to build the model.
Write the missing numerator.
9
6
 ​ = ​ ___   ​ 
1.​ __
8
12
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
4
8
2.​ ___
  ​ = ​ __  ​
5
10
1
​ ___
10  ​ 
1 ​
​ __
5
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
__
​  1
5 ​
__
​  1
5 ​
__
​  1
5 ​
Use Fraction Towers to model the given fraction
and equivalent fraction. Draw your model. Write
the missing numerator.
4
3
1
3.​ __
 ​ = ​ ___   ​ 
3
12
__
​  1
3 ​
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
6
4.​ ___
  ​ = ​ __  ​
6
12
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1
___
​  12  ​ 
1 ​
​ __
6
__
​  1
6 ​
__
​  1
6 ​
© ETA hand2mind™
Find the equivalent fraction. Write the missing numerator.
4
2
 ​ = ​ ___   ​ 
5.​ __
5
10
Equivalent Fractions and Decimals ■ Lesson 1
1
3
6. ​ ___
  ​ = ​ __  ​
4
12
4
8
7.​ ___
  ​ = ​ __  ​
6
12
Hands-On Standards® Fractions
Name Answer Key
2
What fraction of the rectangle is shaded?
2 ​ or __
ANSWER: ​ __
​  1 ​
4
2
COMMENTS & EXTENSIONS: This is not a very common
picture of __
​ 1 ​. Given a rectangle such as the one shown here,
2
what other pictures of __
​ 1 ​can students produce?
2
© ETA hand2mind™
Equivalent Fractions and Decimals ■ Lesson 2
Hands-On Standards® Fractions
Lesson
2
Name Same Height, Fewer Cubes
Answer Key
Try This
■■
Model the first fraction using Fraction Tower Cubes.
■■
Use color hints to model an equivalent fraction in simplest form.
■■
Fill in the answer blanks.
8
1.​ ___
  ​ =
12
2
1
2
2. ​ __
 ​ = ​ __  ​
4
8
​ __
  ​
3
black
2
8 _______­
= ___
orange
2
1
yellow
___
blue = ___
_______
Model
equivalent
fraction.
1
3
9
  ​ = ​  __  ​
3.​ ___
12
4
Model
first
fraction.
9
3
yellow
___
black = ___
_______
2
  ​ = ​  __ 
4.​ ___
10
5
 ​
2
purple
1
green
___
_______
= ___
_______
1
5
  ​ = ​  __ ​
5.​ ___
10
1
6
  ​ = ​  __ ​
6.​ ___
12
5
10
  ​ = ​  __ ​
7.​ ___
12
5
5
 ​ = ​  __ ​
8.​ __
6
3
6
 ​ = ​  __ ​
9.​ __
8
7
7
  ​ = ​  __ ​
10.​ ___
10
2
2
6
6
4
10
4
8
​ ___
  ​ = ​  __ ​
10
5
__
​  69 ​ =
2
​  __ ​
3
Equivalent Fractions and Decimals ■ Lesson 2
9
9
​ ___
  ​ = ​  __ ​
10
10
© ETA hand2mind™
Challenge
Find an equivalent fraction without using cubes.
Show your work.
__
​  46 ​ =
2
​  __ ​
3
1
4
​ ___
  ​ = ​  __ ​
12
3
Hands-On Standards® Fractions
Lesson
2
Name Same Height, Fewer Cubes
Answer Key
Use Fraction Towers to build the model. Write the
missing numerator to rename the fraction.
3
6
 ​ = ​ __  ​
1.​ __
4
8
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
__
​  1
8 ​
2
4
2.​ ___
  ​ = ​ __  ​
5
10
1 ​
​ __
4
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
__
​  1
4 ​
__
​  1
5 ​
__
​  1
5 ​
__
​  1
4 ​
Use Fraction Towers to model the given fraction
and the equivalent fraction in simplest form.
Draw your model. Write the fraction.
__
​  1​ 
5
2
3.​ ___
  ​ = _______
10
__
​  2​ 
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
1  ​ 
___
​  10
8
3
4.​ ___
  ​ = _______
12
__
​  1
2 ​
1  ​ 
___
​  12
1  ​ 
___
​  12
1  ​ 
___
​  12
1  ​ 
___
​  12
1  ​ 
___
​  12
1  ​ 
___
​  12
1  ​ 
___
​  12
1  ​ 
___
​  12
__
​  1
3 ​
__
​  1
3 ​
© ETA hand2mind™
Write the fraction in simplest form.
__
​  5​ 
10
6
  ​= _______
5.​ ___
12
Equivalent Fractions and Decimals ■ Lesson 2
__
​  3​ 
6
5
6. ​ ___
  ​ = _______
10
__
​  3​ 
9
4
7.​ ___
  ​ = _______
12
Hands-On Standards® Fractions
Name Answer Key
3
Can these be shared equally among 3 people?
a. 8 chairs
b. 12 pens
c. 20 pennies
ANSWER: a. no; b. yes; c. no
COMMENTS & EXTENSIONS: Note that all these items are
usable only in whole units. (Pens cannot be cut into meaningful
pieces.) If the materials were liquids, like gallons of milk, the
answers would be different.
© ETA hand2mind™
Equivalent Fractions and Decimals ■ Lesson 3
Hands-On Standards® Fractions
Lesson
3
Name More Than a Whole Square
Answer Key
Try This
5 thirds
■■
Choose the appropriate Fraction Square
pieces to model the problem.
■■
Draw and color the fraction parts on
the squares shown.
■■
Write the fraction and the mixed number.
1. 3 halves
__
​  3 ​
1 __
1 __
1 __
1
__
__
​  1
3 ​ ​  3 ​ ​  3 ​ ​  3 ​ ​  3 ​
5
​ __
 ​
3
fraction
2. 5 fourths
1 ​
1​ __
1 __
1 __
1 __
1 __
1
__
__
​  1
3 ​ ​  3 ​ ​  3 ​ ​  3 ​ ​  3 ​ ​  3 ​
2
1​ __
 ​
3
mixed number
3. 4 thirds
__
​  5 ​
1 ​
1​ __
__
​  4 ​
1 ​
1​ __
2
2
4
4
3
3
__________
= __________
__________
= __________
__________
= __________
fraction
mixed number fraction
mixed number fraction
mixed number
4. 7 fifths
__
​  75 ​
5. 11 eighths
2 ​
1​ __
5
___
​  11 ​ 
8
6. 11 tenths
3
1​ __
 ​
8
___
​  11  ​
10
1  ​ 
1​ ___
10
__________ = __________ __________ = __________ __________ = __________
fraction
mixed number fraction
mixed number fraction
mixed number
7. 8 thirds
2 ​
2​ __
3
__________ = __________
fraction
mixed number
Equivalent Fractions and Decimals ■ Lesson 3
___
​  11 ​ 
4
3
2​ __
 ​
4
__________ = __________
fraction
mixed number
Hands-On Standards® Fractions
© ETA hand2mind™
__
​  8 ​
3
8. 11 fourths
Lesson
3
Name More Than a Whole Square
Answer Key
Use Fraction Squares to build the model. Write the number
the model represents as a fraction and as a mixed number.
1. 3 halves
2. 7 fourths
__
​  3​ 
1 ​
1​ __
fraction
mixed number
2
2
__________
= __________
__
​  7​ 
3
1​ __
 ​
fraction
mixed number
4
4
__________
= __________
Use Fraction Squares to model the number. Draw the
model on the squares shown. Write the number as a
fraction and as a mixed number.
3. 5 thirds
4. 8 fifths
5. 7 sixths
__
​  5​ 
2 ​
1​ __
__
​  8​ 
3
1​ __
 ​
__
​  7​ 
1 ​
1​ __
3
3
5
5
6
6
__________
= __________
__________
= __________
__________
= __________
fraction
mixed number fraction
mixed number fraction
mixed number
Draw a model of the number on the squares shown.
Write the number as a fraction and as a mixed number.
7. 9 fourths
__
​  5​ 
1 ​
2​ __
2
2
__________
= __________
fraction
mixed number
Equivalent Fractions and Decimals ■ Lesson 3
© ETA hand2mind™
6. 5 halves
__
​  9​ 
1 ​
2​ __
4
4
__________
= __________
fraction
mixed number
Hands-On Standards® Fractions
Name Answer Key
4
a.What fraction is shaded?
1
A. ___
​  10
  ​ 
1
B. ___
​  20
  ​ 
C. __
​  12 ​
1
D. ​ __
 ​
4
b. Shade the same fraction of this shape.
ANSWER: a. ___
​  1  ​; 
10
b. Sample:
COMMENTS & EXTENSIONS: A question for students: Where
in real life do you run across the fraction __
​ 1 ​? Where do you find __
​ 1 ​?
2
4
What is the most common fraction you can find in real life?
Give 3 examples of where this fraction shows up in real life.
© ETA hand2mind™
Equivalent Fractions and Decimals ■ Lesson 4
Hands-On Standards® Fractions
Lesson
4
Name Fractions and Decimals
Answer Key
Try This
■■
Use Base Ten Blocks to model
each fraction.
■■
Choose a tenths or hundredths
grid to draw the fraction.
Label the grid with its corresponding
problem number.
■■
Fill in the blanks with the decimal
name, fraction, or decimal for
each problem.
___
​  2  ​ 
10
4 tenths
43 hundredths
4
  ​ = 0.4
​ ___
10
43
​ ___
  ​ = 0.43
100
0.2
1. 2 tenths
= _______ = _______
fractiondecimal
27
___
​  100
   
​
hundredths
0.27
2. 27 ________________=
_______
= _______
fractiondecimal
____
​  20  ​ 
100
0.20
3. 20 hundredths
= _______ = _______
fractiondecimal
tenths
___
​  6  ​ 
10
hundredths
____
​  68  ​ 
100
0.6
4. 6 ________________ = _______ = _______
fractiondecimal
0.68
5. 68 ________________= _______ = _______
fractiondecimal
____
​  33  ​ 
100
0.33
6. 33 hundredths
= _______ = _______
fractiondecimal
© ETA hand2mind™
9
​ ___
    
​
hundredths
0.09
100
7. 9 ________________ = _______
= _______
fractiondecimal
___
​  10  ​
10
1
8. 10 tenths
= _______ = _______
fractiondecimal
Equivalent Fractions and Decimals ■ Lesson 4
Hands-On Standards® Fractions
Lesson
4
Name Fractions and Decimals
Answer Key
Use Base Ten Blocks to build the model. Write the
number as a fraction and as a decimal number.
___
​  3  ​ 
10
0.3
1. 3 tenths = __________ = __________
fractiondecimal
____
​  35  ​ 
100
0.35
2. 35 hundredths = ________ = ________
fractiondecimal
Use Base Ten Blocks to model the number. Draw the
model by shading the grid. Fill in the blanks.
___
​  6  ​ 
10
____
​  27  ​ 
100
3. 6 tenths = __________ = __________
fractiondecimal
0.27
4. 27 hundredths = ________ = ________
fractiondecimal
18
hundredths
0.18
5. 18 __________
= ____
​ 100
  ​ = __________
fractiondecimal
hundredths
100
6. 42 __________
= __________
= 0.42
fractiondecimal
0.6
____
​  42  ​ 
© ETA hand2mind™
Equivalent Fractions and Decimals ■ Lesson 4
Hands-On Standards® Fractions